In a recording disc cartridge of the above type, a floppy disc sheet is rotatably enclosed in a disc case made of a generally hard case with liners made of non woven material interposed between the inner surfaces of the disc case and the floppy disc sheet. In a case where the liners are so laid in the disc case as to slidably uniformly contact with the over all recording face of the disc sheet, there is required a great torque to drive the disc sheet, relative to a low cleaning effect. In order to lower the required rotational torque while still maintaining a good cleaning effect, the liners are provided so that a part of the liners strongly contact the disc sheet. In employing such a configuration it is required to avoid head touch i.e., the state of contact between the magnetic head and the disc sheet is not badly harmed by the deformation of the disc sheet due to the local pressure contact between the liner and the disc sheet. For this purpose, it has been known to provide a protruded portion 14 at the furthest portion rearwardly away from the head insertion hole in the disc case as shown FIG. 2, so as to press the liner to the disc sheet on the protruded portion. Even in this arrangement, during rotation of the disc sheet, the disc sheet may be flapped at an intermediate portion between the protruded portion 14 and the head insertion window 4. Furthermore, since deformation of the disc sheet due to the local pressure contact of the disc sheet onto the liner at the protruded portion remains, good head touch is diminished, whereby there may occur tracking errors and/or distortion of the output signal.